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Nash Embedding and Equilibrium in Pure Quantum States

  • Faisal Shah KhanEmail author
  • Travis S. Humble
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11413)

Abstract

With respect to probabilistic mixtures of the strategies in non-cooperative games, quantum game theory provides guarantee of fixed-point stability, the so-called Nash equilibrium. This permits players to choose mixed quantum strategies that prepare mixed quantum states optimally under constraints. We show here that fixed-point stability of Nash equilibrium can also be guaranteed for pure quantum strategies via an application of the Nash embedding theorem, permitting players to prepare pure quantum states optimally under constraints.

Keywords

Nash embedding Fixed-point stability Nash equilibrium 

Notes

Acknowledgments

Faisal Shah Khan is indebted to Davide La Torre and Joel Lucero-Bryan for helpful discussion on the topic of fixed-point theorems.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Center on Cyber-Physical Systems and Department of MathematicsKhalifa UniversityAbu DhabiUnited Arab Emirates
  2. 2.Quantum Computing Institute, Oak Ridge National LabOak RidgeUSA

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